On the Modelling of Price Effects in the Diffusion of Optional Contingent Products

Abstract

In this chapter, we study the pricing strategies of firms in a multi-product diffusion model where we use a new formalization of the price effects. More particularly, we introduce the impact of prices on one of the factors that affect the diffusion of new products: the innovation coefficient. By doing so, we relax one of the hypotheses in the existing literature stating that this rate is constant. In order to assess the impact of this functional form on the pricing policies of firms selling optional contingent products, we use our model to study two scenarios already investigated in the multiplicative form model suggested by Mahajan and Muller (1991) (M&M). We follow a ‘logical experimentation’ perspective by computing and com- paring the results of three models: (i) The M&M model, (ii) a modified version of M&M where the planning horizon is infinite, and (iii) our model, where the new formalization of the innovation effect is introduced. This perspective allows us to attribute the differences in results to either the length of the planning horizon, or to our model’s formalization. Besides its contribution to the literature on pricing and diffusion, this paper highlights the sensitiv- ity of results to the hypothesis used in product diffusion modelling and could explain the mixed results obtained in the empirical validations of diffusion models (Mesak, 1996).